A continuous finite element solution of fluid interface propagation for emergence of cavities and geysering

Abstract

A finite element method integrated with flux correction techniques is presented for the solution of two nearly incompressible fluids flow with moving interfaces. The procedure incorporates the advection of a phase function to couple fluids motion and the contact discontinuity, and a modified continuity equation preserving mass conservation by considering the parametric definition of density. Limiting bounds comprise information of interface location, improving responses for flows with low density ratio between fluids. A simple conservative postprocessing restores interface resolution by means of an anisotropic streamlined diffusion equation. Strategies to decrease transition thickness between two fluids are examined, using as background the stability of artificial stratified flows and mass error estimation due to density interpolation. To decrease transition thickness, a novel inexpensive nested-grid refinement is proposed. The method is founded in flux-correction principles, ensuring conservation and monotonicity of the variables during dynamical adaptation. Numerical experiments explore the efficacy of the procedure for demanding tests of phase transport and of the equations of motion for interface problems. The main target of this work is to model the genesis and propagation of air cavities in water pipe flows, thus a substantial part of testing focuses on these challenging phenomena. Weakly compressible fluid assumption is essential for proper momentum transfer between phases in the aforementioned dynamics, particularly for bubble rising process. An axisymmetric solution is also developed as an alternative cost-effective choice of the full three-dimensional model for flows in circular ducts.